中英文日报导航站 ,Chapter 7,Inviscid, Compressible Flow,With the realization of airplane and missile speeds equal to or even surpassing the many times the speed of sound, thermodynamics has entered the scene and will never again leave our consideration.,中英文日报导航站 ,7.1 Introduction,Giving the main differences between the incompressible and compressible flows with respect to aerodynamic properties .,What flow properties should be introduced for the analysis of compressible flow problems.,This chapter relates interesting, historical events dating back to the birth of modern aerodynamics; I advice all students to read this chapter carefully.,中英文日报导航站 ,Definition of compressible flows; The position of analysis of compressible flows in our textbook; The change between kinetic energy and internal energy should be taken into account; A High Speed Flow is a High Energy Flow; The change between kinetic energy and internal energy should be considered under the science of thermodynamics; Road map of this chapter,中英文日报导航站 ,7.2 A BRIEF REVIEW OF THERMODYNAMICS,7.2.1 PERFECT GAS,A gas is a collection of particles that are in more or less random motion. If these particles are far enough apart, the influence of intermolecular forces can be neglected; this gas is defined as a perfect gas for which p, and T are related through the equation of state:,中英文日报导航站 ,where R is the specific gas constant ; for air at standard conditions, R = 287 J/(kg.K). This formula can also be written as:,where is the specific volume (volume per unit mass);,中英文日报导航站 ,7.2.2 INTERNAL ENERGY AND ENTHALPY,Consider a molecule: its velocity and its rotational motion create kinetic energy its vibration creates vibrational energy the motion of electrons around the nuclei creates electronic energy,中英文日报导航站 ,The energy of a given molecule is the sum of these energies. Consider a finite volume of gas consisting of a large number of molecules. The sum of the energies of all the molecules in this volume is defined as the internal energy of the gas. Per unit of mass, it is denoted as . A related quantity is the specific enthalpy, denoted by and defined as:,中英文日报导航站 ,For a perfect gas, both and are functions of temperature only:,If and represent differentials of and , respectively; then, for a perfect gas :,and are the specific heats at constant volume and constant pressure, respectively,中英文日报导航站 ,For a perfect gas where these specific heats are constants , the above formula become:,In this case, the gas is called calorically perfect gas. calorically perfect gas : 量热完全气体,Some explanation for the thermodynamic state variables, and specially for specific heats,中英文日报导航站 ,e and h are thermodynamic state variables, they depend only on the state of the gas and are independent of any process. Now, we have the thermodynamic variables as follows: P : pressure : density T : temperature e : internal energy h : enthalpy,中英文日报导航站 ,For a specific gas, we have the following equations:,Define . For air at standard conditions, . Then we get particularly useful equations:,or,or,中英文日报导航站 ,Similarly, dividing the above equation by,中英文日报导航站 ,7.2.3 FIRST LAW OF THERMODYNAMICS,Consider a fixed mass of gas called system. The region outside the system is called surroundings, the interface is called boundary.,中英文日报导航站 ,Assume that the system is stationary. is an incremental amount of heat added to the system across the boundary; denotes the work done on the system by the surroundings. The system has an internal energy; the heat added and work done cause a change in energy. Since the system is stationary, this change is simply :,This is the first law of thermodynamics.,中英文日报导航站 ,Hence is an exact differential, its value depend only on the initial and final states of the system, is a state variable. In contrast, and depend on the process in going from the initial to the final states.,We consider 3 types of processes: Adiabatic process: no heat is added or taken away from the system. Reversible process: no dissipative phenomena occur; effects of viscosity, thermal conductivity, and mass diffusion are absent. Isentropic process: this process is both adiabatic and reversible,中英文日报导航站 ,For a reversible process, , where is an incremental change in the volume due to a displacement of the boundary; thus Eq. (7.11) becomes,中英文日报导航站 ,7.2.4 ENTROPY AND THE SECOND LAW OF THERMODYNAMICS,Reason for introducing the entropy ?,Let us define a new state variable, the entropy, as follows:,where is the entropy of the system, is an incremental amount of heat added reversibly to the system, and is the system temperature.,Entropy is a state variable,中英文日报导航站 ,How to add the heat to the system, reversibly ?,Reversible process: no dissipative phenomena occur; effects of viscosity, thermal conductivity, and mass diffusion are absent.,More detailed definition of Reversible process,Equilibrium state and quasi equilibrium process 平衡状态 与 准平衡过程,中英文日报导航站 ,Entropy is a sta